I am reading "Linear System Theory and Design" by Chen and he says (in what follows g(t,tau) is the impulse response function): If a system is causal, the output will not appear before an input is applied. Thus we have Causal <==> g(t,tau) = 0 for t < tau. However, this seems incorrect to me. For a given tau, g(t,tau) represents the output of the system in response to a delta spike centered at t= tau. So, for t < tau, the input stimulating g(t,tau) is 0. The author then concludes from this that the output for t < tau must also be zero. But this is false. Consider for instance a system consisting of a logical NOT gate where your the output is the logical NOT of your input. g(t,tau) would not be zero for t<tau for this system. What am I missing?